Even a rusty chain is ridiculously efficient - in the high 90%'s. An ICE and drive chain is pitiful in comparison, so let's substitute the chain for a missing r

Even a rusty chain is ridiculously efficient - in the high 90%'s. An ICE and drive chain is pitiful in comparison, so let's substitute the chain for a missing rear axle nut so that, when pedalling, the wheel pulls to one side and creates tangible frictional losses. I grew up in a very hilly area plus I have done a few continental rides where hills can be graded nicely and go on for 10 - 20 miles with little change of gradient. The hope to coast up the other side of the valley never really works out as well as one might hope, with a road that goes down a big hill you are invariably pedalling on the lower reaches of the down hill part, even if you were doing a good 30+ mph at the top. This can be due to the valley heating during the day giving a prevailing headwind due to air expanding. Meanwhile, in the steep hills I grew up in, you can get a measured 40+ mph, conservative guessing (I would be boasting if I mentioned top measured speeds as they can be quite incredible but 40 mph is the town limits speed and it is cool to exceed it on a bike). Clearly this speed scrubs off with aerodynamics not being favourable. So you really do not blissfully roll up the other side, roller-coaster style. On a daily basis I go over an arched bridge that does have a hill leading in to it. So you can coast down the hill, up over the arch and on down the other side. The fun is to not pedal over the bridge, to be in 'roller-coaster' mode. This feels good, and easy, but there is a psychological factor going on here. One's brain is distracted by the 'roller coaster' (or traffic) and not really noticing how much of a slog things are. Essentially the only way things could work out anywhere near how you imagine is if there is no atmosphere. The cost of speed is aero and you just do not get the free ride up the other side of the valley, period. If it was quicker/more efficient to go up and down hills we wouldn't have land speed records be they by bicycle or rocket car set on dead-flat courses, would we? With the sibling reply regarding undulating paths, that is part 'mind trick' as it is mentally stimulating going up and down like that. It is just an illusion... However, I can in part rescue your line of thinking on this - muscle groups... I actually like hills and you can use your arms, legs and plenty of muscles in between to 'conquer' a hill. On the flat you are more likely to just spin (unless sprinting). Maybe if you factor in the baseline power your body needs for pumping blood around, maybe that could make things 'possible'. But the more I think about it - no... Look at motorways and trucks. Trucks are more efficient than cars even if they have lots of wheels and no obvious aerodynamic considerations. Lorry drivers do not choose the undulating 'A road next to the motorway when one is available. They stay on the motorway doing their most efficient speed (as that is how to make a profit). Hills that any car or lorry could go up are cut through with motorways, to make things as flat as possible.